What characteristics do all of these have in common: Beowulf, King Arthur, John the Carpenter, the knight in The Wife of Bath's Tale, Mak, Sir Gawain, the Green Knight, Grendel, and Unferth?
One characteristic common to all is that they are male. This could lead to an interesting discussion of the historical and social contexts in which these works were written.
I believe I benefited greatly from studying English Literature as an undergraduate. It helped me understand the sociological aspects of our world history and to put historical events into perspective.
Through literature, you can examine an era and see how the world was viewed by the people of that time. Going further, and studying less popular works, can help you grasp what was taken as "this is the way it is" and what might have been challenged by some as not "the way it is."
I am puzzled by your assignment as you have listed an extreemely diverse set of characters, encompassing heroes to villains, and also the animal kingdom (Grendel) to the human (Beowulf/King Arthur.) Also the list goes from the natural (humans like King Arthur) to the supernatural (Grendel) and the mortal (Beowulf) to the almost immortal (Grendel.) I think all you can do in these circumstances is to make separate lists under the titles I have given you and place each name under the 'right' heading! The other thing you could try is just to band all of them together under a very loose band of 'they are all legendary characters!'